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If O A B C is a tetrahedron where O is t...

If `O A B C` is a tetrahedron where `O` is the origin and `A ,B ,a n dC` are the other three vertices with position vectors, ` vec a , vec b ,a n d vec c` respectively, then prove that the centre of the sphere circumscribing the tetrahedron is given by position vector `(a^2( vec bxx vec c)+b^2( vec cxx vec a)+c^2( vec axx vec b))/(2[ vec a vec b vec c])` .

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